Abou El Magd A. Mohamed

Nonlinear electrohydrodynamic Rayleigh–Taylor instability. Part 1. A perpendicular field in the absence of surface charges

Nonlinear electrohydrodynamic Rayleigh-Taylor instability is investigated. A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal electric field is subjected to nonlinear deformations. We use the method of multiple-scale perturbations in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable from unstable flows. We obtain two nonlinear Schrodinger equations by means of which we can deduce the cutoff wavenumber and analyse the stability of the system. It is found that if a finite-amplitude wave exists then its small modulation is stable. We also obtain the surface elevation for such waves. The electric field plays a dual role in the stability criterion and the dielectric constant plays a distinctive role in this analysis. If the dielectric constant of the upper fluid is smaller than that of the lower fluid the field has a destabilizing effect for large wavenumbers. For relatively smaller wavenumbers the electric field stabilizes considerable parts of the first and second subharmonic regions in the stability diagrams; a result which is in contrast with the linear theory. If the dielectric constant of the upper fluid is larger than that of the lower fluid, then the field is stabilizing for larger values of the wavenumber K′ when ρ is small (ρ is the density ratio) and destabilizing for smaller values of K′.

Nonlinear electrohydrodynamic Rayleigh–Taylor instability. II. A perpendicular field producing surface charge

The nonlinear electrohydrodynamic stability of two superposed dielectric fluids is studied. The system is stressed by a normal electric field such that it allows for the presence of surface charges at the interface. The method of multiple scale perturbations is used to obtain two nonlinear Schrodinger equations describing the behavior of the disturbed system. The stability of the perturbed system is discussed both analytically and numerically and stability diagrams are obtained. The electric field plays a dual role in the sense that it can stabilize the system for relatively large values of wavenumbers and small values of the density ratio and vice versa. The stabilizing range of the electric field for some given density ratios is tabulated. The analogy with hydromagnetic stability is established. Expressions for the surface elevation and the cutoff wavenumber separating stable and unstable disturbances are also obtained.

Nonlinear electrohydrodynamic Kelvin-Helmholtz instability: effect of a normal field producing surface charges

The electrohydrodynamic stability of a horizontal interface separating two dielectric streaming fluids stressed by a normal electric field is studied. The interface is assumed to support surface charges. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions. Two nonlinear Schrodinger equations describing the perturbed system are obtained. The electrohydrodynamic cutoff wavenumber separating stable and unstable disturbances is calculated. It is found that both streaming and electric field play a dual role on the stability criterion. It is possible that the destabilising effect of streaming can be supressed by the stabilizing effect of the electric field and vice versa. Electrohydrodynamic solitary waves are also discussed.

Electrohydrodynamic stability of a fluid layer. II. Effect of a normal electric field

The electrodynamic stability of two interfaces separating three fluids is studied. A linear model allowing general surface deformations is applied. The case where there are no surface charges present at the interfaces showed a destabilizing influence of the electric field. When there are surface charges on the interface, it is found that the field is still destabilizing but this effect is partially shielded in some situations, which shows some analogy with the nonlinear stability of a single interface.

Electrohydrodynamic stability of two cylindrical interfaces under the influence of a tangential periodic electric field

The electrohydrodynamic stability of two cylindrical interfaces influenced by a periodic tangential field is studied. The model allows for general forms of deformations of the interfaces. Two simultaneous ordinary differential equations of the Mathieu type are obtained. The coupled equations are solved by the method of multiple scales and stability conditions are discussed. It is found that the constant tangential field has a stabilizing effect while the tangential periodic field has a stabilizing influence except at resonance points. Graphs are drawn to illustrate the resonance regions in a parameter space. It is also found that the thickness of the jet plays a role in the stability criterion. The frequency of the modulated field can be used to control the position of the resonance regions. The special cases of large modulation and small modulation are also examined. It is found that for large modulation the electric field exhibits an enhanced destabilizing influence.

Nonlinear electrohydrodynamic Kelvin-Helmholtz instability with mass and heat transfer. Effect of a tangential field

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed dielectric fluids with interfacial transfer of mass and heat is presented for layers of finite thickness. The fluids are subjected to a tangential electric field. The method of multiple scale perturbations is used to obtain a dispersion relation for the first-order problem and a Ginzburg-Landau equation, for the higher-order problem, describing the behaviour of the system. The stability criterion is expressible in terms of various competing parameters representing the equilibrium heat flux, latent heat of evaporation, gravity, surface tension, densities of the fluids, dielectric constants of the fluids, thicknesses of the layers and thermal properties of the fluids. The stability of this system is discussed both analytically and numerically and the stability diagrams are obtained.

Electrohydrodynamic stability of a fluid layer. Effect of a tangential periodic field

SummaryThe electrohydrodynamic stability of a fluid layer influenced by a periodic tangential electric field is studied. The model allows for general forms of deformations of the interface. Two simultaneous ordinary differential equations of Mathieu type are obtained. The coupled equations are solved by the method of multiple-scale perturbations for small electric-field amplitude and stability conditions are discussed. It is found that the tangential field has a stabilizing effect except at resonance points. Graphs are drawn to illustrate the resonance regions in a parameter space. The tangential periodic field cannot stabilize a system which is unstable under a constant electric field.RiassuntoSi studia la stabilità elettrodinamica di una strato fluido influenzato da un campo elettrico tangente periodico. II modello tien conto delle forme generali di deformazioni dell’interfaccia. Si ottengono due equazioni simultanee differenziali ordinarie del tipo di Mathieu. Le equazioni accoppiate sono risolte col metodo delle perturbazioni su scala multipla per piccola ampiezza di campo, elettrico e si dicutono le condizioni di stabilità. Si è trovato che il campo tangente, ha un effetto stabilizzante eccetto nei punti di risonanza. I grafici sono fatti per illustrare le regioni di risonanza in uno spazio di parametri. Il campo periodico tangente non può stabilizzare un, sistema che è instabile in un campo elettrico costante.

Effect of general applied electric field on conducting liquid jets instabilities in the presence of heat and mass transfer

A novel system to study the effect of general applied electric field on the stability of a cylindrical interface between the vapor and liquid phases of conducting fluids in the presence of heat and mass transfer is investigated. The vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relations are obtained and discussed, for both cases of axial and radial constant electric fields, and the stability of the system is analyzed theoretically and numerically for both cases. Some limiting cases in the literature and discussed and recovered. In the former case of axial electric field, both axisymmetric and asymmetric disturbances are considered. It is found, in this case, that the heat and mass transfer, revealed through a single parameter, has no influence on the stability of the system, which is contrary to the stabilizing result obtained earlier for plane geometry. In the later case of radial electric field, it is found that each of the heat and mass transfer, the azimuthal wavenumber, and the dimensions of the system has a stabilizing effect; while the electrical conductivity has a destabilizing influence on the considered system.

Nonlinear Electrohydrodynamic Stability of a Fluid Layer: Effect of a Tangential Electric Field

The weakly nonlinear electrohydrodynamic stability of fluid layer sandwiched between two semi-infinite fluids is investigated. The nonlinear theory of perturbation is applied for symmetric and anti-symmetric modes. The method of multiple scales is used to expand the various perturbation quantities to yield the linear and successive nonlinear partial differential equations of the various orders. The solutions of these equations are obtained. The application of the boundary conditions leads to two nonlinear Schrodinger equations. It is found that the presence of the tangential field plays a stabilizing role and can be used to suppress the instability of the system at a given wavenumber which is unstable linear stability. Numerical calculations show a global stability for certain wavenumbers. A local instability is also observed in the graphs. The field plays a dual role. It is observed that the change of the layer thickness redistributes the stable areas.

Electroviscoelastic Rayleigh-Taylor instability of Maxwell fluids: I. Effect of a constant tangential electric field

The stability of the Rayleigh-Taylor model for an electroviscoelastic Maxwell fluid are investigated. The method of multiple scales is used in order to obtain the stability conditions. A transcendental dispersion relation is obtained at zero-order. The special case, when the two fluids have the same kinematic viscosity, is considered to relax the complexity of the transcendental dispersion relation. The solvability conditions introduce a first-order differential equation. It is found that the increase in the relaxation time lambda has a destabilizing influence. Also the increase in the kinematic viscosity in the presence of the parameter lambda yields a destabilizing effect. The increase in the kinematic viscosity in the absence of elasticity (pure viscous fluids) has a stabilizing effect.